Elementary Algebra for the Use of Preparatory Schools |
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Page ix
... Limits .. 417 Indeterminate Forms .. 421 XXIX . Exponentials and Logarithms ... 426 XXXII . Exponentiation .... Logarithmic Operation . XXX . Natural Logarithms .. XXXI . Convergency and Divergency of Series .. Indeterminate ...
... Limits .. 417 Indeterminate Forms .. 421 XXIX . Exponentials and Logarithms ... 426 XXXII . Exponentiation .... Logarithmic Operation . XXX . Natural Logarithms .. XXXI . Convergency and Divergency of Series .. Indeterminate ...
Page 204
... limits , it is called an infinite quantity , or infinity , and for convenience the special sym- bol is used to represent it . ∞ But this nomenclature must be regarded as conven- tional , and the symbol must be used in algebraic ...
... limits , it is called an infinite quantity , or infinity , and for convenience the special sym- bol is used to represent it . ∞ But this nomenclature must be regarded as conven- tional , and the symbol must be used in algebraic ...
Page 346
... limit of ( a + x ) / ( b + x ) when x is very great , is unity . 240. The following definitions are sometimes required : The ratio of the product of the first terms of any number of ratios to the product of their second terms is called ...
... limit of ( a + x ) / ( b + x ) when x is very great , is unity . 240. The following definitions are sometimes required : The ratio of the product of the first terms of any number of ratios to the product of their second terms is called ...
Page 386
... limit as the number of the operations is increased , the sum of the parts taken away can be made to differ from two inches by a length which is smaller than any conceivable length ; hence , by taking a sufficiently large number of terms ...
... limit as the number of the operations is increased , the sum of the parts taken away can be made to differ from two inches by a length which is smaller than any conceivable length ; hence , by taking a sufficiently large number of terms ...
Page 399
... limit by S ... Ex . 1. Find the sum of n terms of the series 1.2 + 2.3 + 3.4 + 4.5+ ... Here Sn = 1.2 + 2.3 + 3.4 + ... + ( n − 1 ) n + n ( n + 1 ) . Let 2 = 1.2.3 + 2.3.4 + 3.4.5 + ... + ( n − 1 ) n ( n + 1 ) + n ( n + 1 ) ( n +2 ) .
... limit by S ... Ex . 1. Find the sum of n terms of the series 1.2 + 2.3 + 3.4 + 4.5+ ... Here Sn = 1.2 + 2.3 + 3.4 + ... + ( n − 1 ) n + n ( n + 1 ) . Let 2 = 1.2.3 + 2.3.4 + 3.4.5 + ... + ( n − 1 ) n ( n + 1 ) + n ( n + 1 ) ( n +2 ) .
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Common terms and phrases
7th term a²b a²b² a²x a²x² a³b ab² ab³ absolutely convergent algebraical expression arithmetic means ax² b₁ binomial theorem cents CHAPTER coefficients contain continued fraction convergent denote determinant difference digits Divide dividend division divisor equal equation x² example Find the factors Find the H. C. F. Find the number Find the square Find the sum Find the value finite formula geometrical progression given expression greater Hence indeterminate forms integer less letters limit logarithms monomial Multiply negative nth root number of terms obtain permutations positive integer powers Prove quadratic equation quotient remainder result Show Simplify simultaneous equations Solve the equation square root subtract surds unknown quantities x²y x²y² xy² xy³ zero
Popular passages
Page 46 - Multiplication is the process of taking one number as many times as there are units in another number.
Page 362 - Find the area of a circle whose radius is 12 feet, from the law that the area of a circle varies as the square of its radius.
Page 349 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 77 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 362 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".